Basma Fakri, president of the Women's Alliance for a Democratic Iraq, gave several examples of how a strict adherence to Shari'a could hurt women because of the way Koranic law can be interpreted.
"Marriage, multiple marriages: This can be used -- and has been used, and abused -- under the name of Islam," she said. "Minimum age: Certain Islamic sectors allow for the marriage of girls as young as the age of nine. Forceful marriage: Some Sharia interpretations will allow for a guardian to force marriage on a girl against her will."
Fakri said the people now writing Iraq's new constitution should make sure that it is not open to such interpretations.
Another advocate, Tanya Gilly of the Foundation for the Defense of Democracies, said she is often challenged by those who say that the idea of women's equality is too novel for a country like Iraq, so why not leave it unsettled for now and address it after 15 August?
If Iraq waits, Gilly said, then Iraqi women will lose their rights. So she called on Washington to put pressure on the Baghdad panel drafting the document so that equal rights are included in it by the August deadline.
"We want to make sure that the U.S. administration and the Congress maintain the pressure on the Iraqi government and on the constitutional writing committees in order to make sure that we are protected, not just as women but also as individuals," Gilly said. "And we hope that Congress would increase funding for women's programs so it can raise awareness within the country."
Gilly said such appeals are not restricted to the United States. She said her organization and other advocacy groups for women also have been urging similar pressure from Britain, the United Nations, and the European Union.
Fakri said she and her colleagues will continue pressing not only the constitutional committee in Baghdad, but also the U.S. and British governments, as well as the UN and the EU. She said they don't want the panel to lose sight of women's equality when they have so many other issues to consider.
"We keep on pushing because the constitutional committee are overloaded, very busy. So we don't want them to forget one of these demands. We want to keep on reminding them till 15 August," she said.
Another way the activists are putting pressure on Iraq's constitutional commission is to bring up the issue with the news media, as they did yesterday. That sounds like a good idea, according to Nathan Brown, who studies Middle Eastern issues at the Carnegie Endowment for International Peace, a Washington-based policy research center.
Brown, who has written extensively on constitutional issues in the region, says that on the issue of women's rights, the Iraqi advocates must appeal not only to the administration of President George W. Bush, but also to the American public, through the media.
"The real pressure on the women's rights issues -- or the strongest pressure -- doesn't necessarily come from high-level members of the Bush administration themselves, but it comes from the court of American public opinion," Brown told RFE/RL. "And the Bush administration does not want to see an Iraqi constitution that will embarrass it."
In Iraq, women from professional backgrounds have been leaders in pressing for greater rights for women in the new, post-Saddam Hussein order.
But women from traditional backgrounds have been equally active in campaigning for religious parties that support strict interpretations of Shi’ite law.
At present, it is unclear how the committee drafting the constitution will address those varying demands.
For the latest news and analysis on Iraq, see RFE/RL's webpage on "The New Iraq".